Multiple choice

The product of the two numbers is 1500 and their HCF is 10. The number of such possible pairs is:

  1. 1

  2. 3

  3. 4

  4. 2
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D Correct answer
Explanation

Numbers are 10a and 10b where a, b are coprime. Product = 100ab = 1500, so ab = 15. Pairs (a, b) are (1, 15) and (3, 5). Two pairs.

AI explanation

Since the product is 1500 and their highest common factor is 10, let the numbers be 10x and 10y, where x and y are coprime. This gives 100xy = 1500, so xy = 15. The coprime pairs for 15 are (1, 15) and (3, 5), yielding the number pairs (10, 150) and (30, 50). Therefore, there are exactly 2 such possible pairs. The result is 2.

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